GateXAIMLData Structures & Algorithms
  • Chapter 1: Algorithm Analysis
    • Introduction
    • Core Algorithmic Paradigms
    • Analysis Framework
      • Time and Space Efficiency
      • Input Size and Efficiency Analysis
      • Measuring Running Time of Algorithms
      • Order of Growth
    • Asymptotic Notations
      • Asymptotic Efficiency of Algorithms
      • O-Notation (Big-Oh Notation)
      • $\Omega$-Notation (Big-Omega Notation)
      • $\Theta$-Notation (Big-Theta Notation)
      • Relationship Between $O$, $\Omega$, and $\Theta$
      • Little-$o$ Notation
      • Little-$\omega$ Notation
      • Relationship Between $O$, $\Omega$, $\Theta$, $o$, and $\omega$
    • Best Case, Worst Case and Average Case
    • Relation Between $O$, $\Omega$, $\Theta$ and Best, Worst, Average Case
    • Analysis of Non Recursive Algorithms
      • Useful Maths Formulas
      • Mathematical Analysis of Nonrecursive Algorithms
    • Recurrence Relations
      • Substitution Method
      • Recursion Tree Method
      • Extended Master Theorem
    • Analysis of Recursive Algorithms
      • Factorial Function
      • Fibonacci Function
      • Sum of Digits Function
      • Power Function
    • Useful Formulas
  • Chapter 2: Stacks
    • Core Operations
      • Array Implementation
      • Algorithm, Pseudocode and Python Implementation
    • Applications of Stacks
      • Expression Notations: Infix, Postfix, Prefix
      • Infix to Postfix Conversion (Shunting-Yard Algorithm)
      • Postfix Expression Evaluation
      • Infix to Prefix Conversion
      • Prefix Expression Evaluation
      • Prefix to Infix Conversion
      • Postfix to Prefix Conversion
      • Prefix to Postfix Conversion
      • Balanced Parentheses / Brackets Check
      • Recursion and Call Stack Frames
  • Chapter 3: Queues
    • Core Operations
      • Array Implementation of Queue
      • Circular Queue
      • Deque (Double-Ended Queue)
    • Applications of Queues
  • Chapter 4: Linked Lists
    • Singly Linked List
      • Singly LL --- Insertion Operations
        • Insert at Head
        • Insert at Tail (End)
        • Insert at Middle (Given Position)
      • Singly LL --- Deletion Operations
      • Singly LL --- Search Operation
      • Singly LL --- Reversal
        • Iterative Reversal
        • Recursive Reversal
    • Doubly Linked List
      • Doubly LL --- Insertion Operations
        • Insert at Head
        • Insert at Tail (End)
        • Insert at Middle (Given Position)
      • Doubly LL --- Deletion Operations
        • Delete at Head
        • Delete by Value
        • Delete by Position
      • Doubly LL --- Search Operation
    • Circular Linked List
      • Circular LL --- Insertion Operations
        • Insert at Head
        • Insert at Tail (End)
        • Insert at Middle (Given Position)
      • Circular LL --- Deletion Operations
        • Delete at Head
        • Delete by Value --- First Occurrence
        • Delete by Value --- All Occurrences
        • Delete by Position
      • Circular LL --- Search Operation
    • Classic Problems
      • Floyd's Cycle Detection Algorithm
      • Finding the Start of a Cycle
      • Finding the Middle Node
      • Merge Two Sorted Linked Lists
      • Nth Node from the End
      • Intersection of Two Linked Lists
      • Methods to Find Intersection
        • Method 1: Using Length Difference
        • Method 2: Two-Pointer Redirect Method (Floyd-like)
    • Linked List Implementation of Stack and Queue
      • Stack Using Linked List
      • Queue Using Linked List
  • Chapter 5: Trees
    • Terminology and Structure
      • Full, Complete, and Perfect Binary Tree
      • Array Representation of a Binary Tree
    • Binary Tree Formulas
      • Formula Practice Problems
    • Theorems and Structural Properties of Binary Trees
      • Full Binary Tree
        • Derivation of Full Binary Tree Formulas
      • Perfect Binary Tree
        • Derivation of Perfect Binary Tree Formulas
      • Complete Binary Tree
        • Derivation of Complete Binary Tree Formulas
    • Binary Tree Traversals
      • Inorder Traversal (Left, Root, Right)
      • Preorder Traversal (Root, Left, Right)
      • Postorder Traversal (Left, Right, Root)
      • Reconstructing a Tree from Two Traversals
    • Binary Search Tree (BST)
      • Construct a BST from a Given Insertion Sequence
      • Search in BST
      • Insert in BST
      • Inorder Successor and Predecessor
      • Delete in BST: Three Cases
      • Inorder Traversal of BST Gives Sorted Order
      • Height of BST: Best and Worst Case
      • Number of Distinct BSTs: Catalan Numbers
  • Chapter 6: Hash Tables
    • Hash Functions and Load Factor
      • Division Method
      • Multiplication Method
      • Load Factor
    • Collision Resolution
      • Chaining (Separate Chaining)
      • Open Addressing
        • Linear Probing
        • Quadratic Probing
        • Double Hashing
    • Performance Analysis
GateXAIML · DSA Concept Notes

Data Structures & Algorithms

Chapter 1
Algorithm Analysis
31 sections
Introduction, Core Algorithmic Paradigms, Analysis Framework...
Chapter 2
Stacks
14 sections
Core Operations, Applications of Stacks
Chapter 3
Queues
5 sections
Core Operations, Applications of Queues
Chapter 4
Linked Lists
44 sections
Singly Linked List, Doubly Linked List, Circular Linked List...
Chapter 5
Trees
26 sections
Terminology and Structure, Binary Tree Formulas, Theorems and Structural Properties of Binary Trees...
Chapter 6
Hash Tables
11 sections
Hash Functions and Load Factor, Collision Resolution, Performance Analysis
GateXAIML · Data Structures & Algorithms — Concept Notes
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